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Find the arithmetic mean of all roots of the following equation

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SteveNew
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Find the arithmetic mean of all roots of the following equation [#permalink] New post   Updated on: 28 Apr 2020, 00:16
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Find the arithmetic mean of all roots of the following equation

\((x+2) \sqrt{x-x^2}=0\)

A) 2
B) 1
C) 0.5
D) -1/3
E) 0.3
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C

Originally posted by SteveNew on 25 May 2011, 13:38.
Last edited by Bunuel on 28 Apr 2020, 00:16, edited 6 times in total.
Renamed the topic and edited the tags.
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Re: Find the arithmetic mean of all roots of the following equation [#permalink] New post   28 Apr 2020, 00:16
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MariaAntony wrote:
app219 wrote:
SteveNew wrote:
Find the arithmetic mean of all roots of the following equation

\((x+2) \sqrt{x-x^2}=0\)

A) 2
B) 1
C) 0.5
D) -1/3
E) 0.3


Why is -2 considered a solution? the square root of a negative number doesn't exist, if you plugg in back in the equation this is impossible...
Hence, only possible solutions are 0 and 1; so C

Can someone help?


+1

Can someone please explain why -2 is a valid root of this equation in-spite of having a negative square root in the expression?


-2 is not a valid root. Even roots from negative numbers are not defined on the GMAT. So, only 0 and 1 are valid and the average is 1/2, not -1/3.

Answer: C.

P.S. Not only this is not a GMAT Prep question as it was tagged but also it is not from any reliable GMAT source.
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agdimple333
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Re: Find the arithmetic mean of all roots of the following equation [#permalink] New post   25 May 2011, 18:36
SteveNew wrote:
Hello Guys,

Find the arithmetic mean of all roots of the following equation- see an attachment.

A 2
B 1
C 0.5
D -1/3
E 0.5

Thanks,
Steve.

your answer C and E are same, can you correct one of them please. thanks.
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Re: Find the arithmetic mean of all roots of the following equation [#permalink] New post   25 May 2011, 18:45
Thank you so much Agdimple,

It was corrected.

Steve.
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Re: Find the arithmetic mean of all roots of the following equation [#permalink] New post   25 May 2011, 23:18
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I am getting D.

Equation is \((x+2) \sqrt{x-x^2}=0\)
x+2=0 or x=-2
\(\sqrt{x-x^2}=0\)
x-x^2=0
x(1-x)=0
or x=0
or x=1

Average of all roots= -2+0+1/3=-1/3.
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Re: Find the arithmetic mean of all roots of the following equation [#permalink] New post   25 May 2011, 23:38
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the solutions are x = -2,0 and 1
the mean = -1/3.
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Re: Find the arithmetic mean of all roots of the following equation [#permalink] New post   14 Dec 2016, 14:54
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Excellent Official Questions.
Here is my solution to this one =>
The roots of the equation will be => {-2,0,1}

Hence the mean => \(\frac{-2+0+1}{3} => \frac{-1}{3}\)
Hence D
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Re: Find the arithmetic mean of all roots of the following equation [#permalink] New post   22 Mar 2019, 17:12
Just to know, is there a possibility o create an eq multiplying both terms?
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Re: Find the arithmetic mean of all roots of the following equation [#permalink] New post   23 Mar 2019, 06:19
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SteveNew wrote:
Find the arithmetic mean of all roots of the following equation

\((x+2) \sqrt{x-x^2}=0\)

A) 2
B) 1
C) 0.5
D) -1/3
E) 0.3


Why is -2 considered a solution? the square root of a negative number doesn't exist, if you plugg in back in the equation this is impossible...
Hence, only possible solutions are 0 and 1; so C

Can someone help?
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MariaAntony
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Re: Find the arithmetic mean of all roots of the following equation [#permalink] New post   27 Apr 2020, 20:56
app219 wrote:
SteveNew wrote:
Find the arithmetic mean of all roots of the following equation

\((x+2) \sqrt{x-x^2}=0\)

A) 2
B) 1
C) 0.5
D) -1/3
E) 0.3


Why is -2 considered a solution? the square root of a negative number doesn't exist, if you plugg in back in the equation this is impossible...
Hence, only possible solutions are 0 and 1; so C

Can someone help?


+1

Can someone please explain why -2 is a valid root of this equation in-spite of having a negative square root in the expression?
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Saiharish98
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Re: Find the arithmetic mean of all roots of the following equation [#permalink] New post   27 Apr 2020, 21:17
-2, 0,1 are roots (-2 is root because 0 * imaginary no. is 0) average=-1/3

Posted from my mobile device
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MDUsman
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Re: Find the arithmetic mean of all roots of the following equation [#permalink] New post   06 May 2020, 13:58
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Whenever any such equation is given one must put the critical points in each other to see if any rule is not broken. If oneself is doubtful then best way is to back process the whole.
Square root of {(x+2)(x-x^2)} = 0
Square root of {x^3 - x^4 +4x -4x^2} = 0
Square root of {x^3(1-x) +4x(1-x)} = 0
Square root of {(x^3+4x)(1-x)} = 0
so;
(x^3+4x)(1-x)>=0
x(x^2+4)(1-x)=0 to find the critical points
x=0 or x=1 or
x^2=-4 this is not possible

so roots are 0 and 1
ans is 0.5
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Re: Find the arithmetic mean of all roots of the following equation [#permalink] New post   10 Jan 2024, 04:15
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Re: Find the arithmetic mean of all roots of the following equation [#permalink]
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